Volume 13, Issue 5
Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems

Feng Chen & Jie Shen

Commun. Comput. Phys., 13 (2013), pp. 1189-1208.

Published online: 2013-05

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  • Abstract

We develop in this paper efficient and robust numerical methods for solving anisotropic Cahn-Hilliard systems. We construct energy stable schemes for the time discretization of the highly nonlinear anisotropic Cahn-Hilliard systems by using a stabilization technique. At each time step, these schemes lead to a sequence of linear coupled elliptic equations with constant coefficients that can be efficiently solved by using a spectral-Galerkin method. We present numerical results that are consistent with earlier work on this topic, and also carry out various simulations, such as the linear bi-Laplacian regularization and the nonlinear Willmore regularization, to demonstrate the efficiency and robustness of the new schemes.


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@Article{CiCP-13-1189, author = {}, title = {Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {5}, pages = {1189--1208}, abstract = {

We develop in this paper efficient and robust numerical methods for solving anisotropic Cahn-Hilliard systems. We construct energy stable schemes for the time discretization of the highly nonlinear anisotropic Cahn-Hilliard systems by using a stabilization technique. At each time step, these schemes lead to a sequence of linear coupled elliptic equations with constant coefficients that can be efficiently solved by using a spectral-Galerkin method. We present numerical results that are consistent with earlier work on this topic, and also carry out various simulations, such as the linear bi-Laplacian regularization and the nonlinear Willmore regularization, to demonstrate the efficiency and robustness of the new schemes.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.101111.110512a}, url = {http://global-sci.org/intro/article_detail/cicp/7270.html} }
TY - JOUR T1 - Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems JO - Communications in Computational Physics VL - 5 SP - 1189 EP - 1208 PY - 2013 DA - 2013/05 SN - 13 DO - http://doi.org/10.4208/cicp.101111.110512a UR - https://global-sci.org/intro/article_detail/cicp/7270.html KW - AB -

We develop in this paper efficient and robust numerical methods for solving anisotropic Cahn-Hilliard systems. We construct energy stable schemes for the time discretization of the highly nonlinear anisotropic Cahn-Hilliard systems by using a stabilization technique. At each time step, these schemes lead to a sequence of linear coupled elliptic equations with constant coefficients that can be efficiently solved by using a spectral-Galerkin method. We present numerical results that are consistent with earlier work on this topic, and also carry out various simulations, such as the linear bi-Laplacian regularization and the nonlinear Willmore regularization, to demonstrate the efficiency and robustness of the new schemes.


Feng Chen & Jie Shen. (2020). Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems. Communications in Computational Physics. 13 (5). 1189-1208. doi:10.4208/cicp.101111.110512a
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